/****************************************************************************
 *
 * Copyright 2017 Samsung Electronics All Rights Reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND,
 * either express or implied. See the License for the specific
 * language governing permissions and limitations under the License.
 *
 ****************************************************************************/
/****************************************************************************
 *
 * Copyright © 2005-2014 Rich Felker, et al.
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 ***************************************************************************/
/****************************************************************************
 * origin: FreeBSD /usr/src/lib/msun/src/e_jn.c
 *
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 *
 * jn(n, x), yn(n, x)
 * floating point Bessel's function of the 1st and 2nd kind
 * of order n
 *
 * Special cases:
 *      y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
 *      y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
 * Note 2. About jn(n,x), yn(n,x)
 *      For n=0, j0(x) is called,
 *      for n=1, j1(x) is called,
 *      for n<=x, forward recursion is used starting
 *      from values of j0(x) and j1(x).
 *      for n>x, a continued fraction approximation to
 *      j(n,x)/j(n-1,x) is evaluated and then backward
 *      recursion is used starting from a supposed value
 *      for j(n,x). The resulting value of j(0,x) is
 *      compared with the actual value to correct the
 *      supposed value of j(n,x).
 *
 *      yn(n,x) is similar in all respects, except
 *      that forward recursion is used for all
 *      values of n>1.
 ***************************************************************************/

/************************************************************************
 * Included Files
 ************************************************************************/

#include <tinyara/compiler.h>
#include <math.h>

#include "libm.h"

#ifdef CONFIG_HAVE_DOUBLE

/************************************************************************
 * Private Data
 ************************************************************************/
static const double invsqrtpi = 5.64189583547756279280e-01;	/* 0x3FE20DD7, 0x50429B6D */

/************************************************************************
 * Public Functions
 ************************************************************************/

double jn(int n, double x)
{
	uint32_t ix;
	uint32_t lx;
	int nm1;
	int sign;
	int i;
	float a;
	float b;
	float temp;

	EXTRACT_WORDS(ix, lx, x);
	sign = ix >> 31;
	ix &= 0x7fffffff;

	if ((ix | (lx | -lx) >> 31) > 0x7ff00000) {	/* nan */
		return x;
	}

	/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
	 * Thus, J(-n,x) = J(n,-x)
	 */
	/* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
	if (n == 0) {
		return j0(x);
	}
	if (n < 0) {
		nm1 = -(n + 1);
		x = -x;
		sign ^= 1;
	} else {
		nm1 = n - 1;
	}
	if (nm1 == 0) {
		return j1(x);
	}

	sign &= n;					/* even n: 0, odd n: signbit(x) */
	x = fabs(x);
	if ((ix | lx) == 0 || ix == 0x7ff00000) {	/* if x is 0 or inf */
		b = 0.0;
	} else if (nm1 < x) {
		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
		if (ix >= 0x52d00000) {	/* x > 2**302 */
			/* (x >> n**2)
			 *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
			 *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
			 *      Let s=sin(x), c=cos(x),
			 *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
			 *
			 *             n    sin(xn)*sqt2    cos(xn)*sqt2
			 *          ----------------------------------
			 *             0     s-c             c+s
			 *             1    -s-c            -c+s
			 *             2    -s+c            -c-s
			 *             3     s+c             c-s
			 */
			switch (nm1 & 3) {
			case 0:
				temp = -cos(x) + sin(x);
				break;
			case 1:
				temp = -cos(x) - sin(x);
				break;
			case 2:
				temp = cos(x) - sin(x);
				break;
			default:
			case 3:
				temp = cos(x) + sin(x);
				break;
			}
			b = invsqrtpi * temp / sqrt(x);
		} else {
			a = j0(x);
			b = j1(x);
			for (i = 0; i < nm1;) {
				i++;
				temp = b;
				b = b * (2.0 * i / x) - a;	/* avoid underflow */
				a = temp;
			}
		}
	} else {
		if (ix < 0x3e100000) {	/* x < 2**-29 */
			/* x is tiny, return the first Taylor expansion of J(n,x)
			 * J(n,x) = 1/n!*(x/2)^n  - ...
			 */
			if (nm1 > 32) {		/* underflow */
				b = 0.0;
			} else {
				temp = x * 0.5;
				b = temp;
				a = 1.0;
				for (i = 2; i <= nm1 + 1; i++) {
					a *= (double)i;	/* a = n! */
					b *= temp;	/* b = (x/2)^n */
				}
				b = b / a;
			}
		} else {
			/* use backward recurrence */
			/*                      x      x^2      x^2
			 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
			 *                      2n  - 2(n+1) - 2(n+2)
			 *
			 *                      1      1        1
			 *  (for large x)   =  ----  ------   ------   .....
			 *                      2n   2(n+1)   2(n+2)
			 *                      -- - ------ - ------ -
			 *                       x     x         x
			 *
			 * Let w = 2n/x and h=2/x, then the above quotient
			 * is equal to the continued fraction:
			 *                  1
			 *      = -----------------------
			 *                     1
			 *         w - -----------------
			 *                        1
			 *              w+h - ---------
			 *                     w+2h - ...
			 *
			 * To determine how many terms needed, let
			 * Q(0) = w, Q(1) = w(w+h) - 1,
			 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
			 * When Q(k) > 1e4      good for single
			 * When Q(k) > 1e9      good for double
			 * When Q(k) > 1e17     good for quadruple
			 */
			/* determine k */
			double t;
			double q0;
			double q1;
			double w;
			double h;
			double z;
			double tmp;
			double nf;
			int k;

			nf = nm1 + 1.0;
			w = 2 * nf / x;
			h = 2 / x;
			z = w + h;
			q0 = w;
			q1 = w * z - 1.0;
			k = 1;
			while (q1 < 1.0e9) {
				k += 1;
				z += h;
				tmp = z * q1 - q0;
				q0 = q1;
				q1 = tmp;
			}
			for (t = 0.0, i = k; i >= 0; i--) {
				t = 1 / (2 * (i + nf) / x - t);
			}
			a = t;
			b = 1.0;
			/*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
			 *  Hence, if n*(log(2n/x)) > ...
			 *  single 8.8722839355e+01
			 *  double 7.09782712893383973096e+02
			 *  long double 1.1356523406294143949491931077970765006170e+04
			 *  then recurrent value may overflow and the result is
			 *  likely underflow to zero
			 */
			tmp = nf * log(fabs(w));
			if (tmp < 7.09782712893383973096e+02) {
				for (i = nm1; i > 0; i--) {
					temp = b;
					b = b * (2.0 * i) / x - a;
					a = temp;
				}
			} else {
				for (i = nm1; i > 0; i--) {
					temp = b;
					b = b * (2.0 * i) / x - a;
					a = temp;
					/* scale b to avoid spurious overflow */
					if (b > 0x1p500) {
						a /= b;
						t /= b;
						b = 1.0;
					}
				}
			}
			z = j0(x);
			w = j1(x);
			if (fabs(z) >= fabs(w)) {
				b = t * z / b;
			} else {
				b = t * w / a;
			}
		}
	}
	return sign ? -b : b;
}

double yn(int n, double x)
{
	uint32_t ix;
	uint32_t lx;
	uint32_t ib;
	int nm1;
	int sign;
	int i;
	float a;
	float b;
	float temp;

	EXTRACT_WORDS(ix, lx, x);
	sign = ix >> 31;
	ix &= 0x7fffffff;

	if ((ix | (lx | -lx) >> 31) > 0x7ff00000) {	/* nan */
		return x;
	}
	if (sign && (ix | lx) != 0) {	/* x < 0 */
		return 0 / 0.0;
	}
	if (ix == 0x7ff00000) {
		return 0.0;
	}

	if (n == 0) {
		return y0(x);
	}
	if (n < 0) {
		nm1 = -(n + 1);
		sign = n & 1;
	} else {
		nm1 = n - 1;
		sign = 0;
	}
	if (nm1 == 0) {
		return sign ? -y1(x) : y1(x);
	}

	if (ix >= 0x52d00000) {		/* x > 2**302 */
		/* (x >> n**2)
		 *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
		 *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
		 *      Let s=sin(x), c=cos(x),
		 *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
		 *
		 *             n    sin(xn)*sqt2    cos(xn)*sqt2
		 *          ----------------------------------
		 *             0     s-c             c+s
		 *             1    -s-c            -c+s
		 *             2    -s+c            -c-s
		 *             3     s+c             c-s
		 */
		switch (nm1 & 3) {
		case 0:
			temp = -sin(x) - cos(x);
			break;
		case 1:
			temp = -sin(x) + cos(x);
			break;
		case 2:
			temp = sin(x) + cos(x);
			break;
		default:
		case 3:
			temp = sin(x) - cos(x);
			break;
		}
		b = invsqrtpi * temp / sqrt(x);
	} else {
		a = y0(x);
		b = y1(x);
		/* quit if b is -inf */
		GET_HIGH_WORD(ib, b);
		for (i = 0; i < nm1 && ib != 0xfff00000;) {
			i++;
			temp = b;
			b = (2.0 * i / x) * b - a;
			GET_HIGH_WORD(ib, b);
			a = temp;
		}
	}
	return sign ? -b : b;
}
#endif
